EDIT: maybe setting a new primary isn't what you realy want to do. please take a look at unique indexes - i think thats waht you want to set on your other columns to make sure they don't occur more than once.

First and foremost, if I'm correct you're defining a compound key? This is usually bad practice. It's better to have an extra ID column and to add a separate constraint to check you have a unique combination. And as codymanix suggested, you need to first alter the column to not have auto_increment anymore and then drop it.